# Goedel's Incompleteness Theorem

arXiv: https://arxiv.org/abs/2112.06641 · HTML: https://mlsanity.com/paper/2112.06641/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 1 of its 22 references that are in the map.
- First posted on arXiv 7 Dec 2021.

## Builds on (most cited first, 1 of 1)

- [mu-Forcing: Training Variational Recurrent Autoencoders for Text Generation](https://mlsanity.com/paper/1905.10072/) (2019)

## Abstract (arXiv)

I present the proof of Goedel's First Incompleteness theorem in an intuitive manner, while covering all technically challenging steps. I present generalizations of Goedel's fixed point lemma to two-sentence and multi-sentence versions, which allow proof of incompleteness through circular versions of the liar's paradox. I discuss the relation of Goedel's First and Second Incompletneness theorems to Goedel's Completeness theorems, and conclude with remarks on implications of these results for mathematics, computation, theory of mind and AI.